The ultimate moment is the design load moment multiplied by code overload factors and strength factors applied for the dead and live load cases. I asume you can use beam tables for a beam on 3 supports to find the max positive moment between supports and the max negative moment at the middle support.

The language used in the question is reminiscent of eurocodes. You need to consider the different factors applied to permanent, dead and imposed loads, and then patterned loading in two diffrent load cases to get the moments you need. Do you know what I am talking about? When you say 'depth', do you mean 'width'? How do the loads given in kN/m transform into kN/m2 ?